ABSTRACT: This paper attempts to develop a prediction model that can be used in line with prescribed laboratory experiments for indirect tensile test such that tensile elastic modulus can be predicted for cement stabilized lateritic soil reinforced with steel fiber using measured properties of the material. The results of the tensile elastic modulus obtained from the Derived Prediction Model almost nearly replicates that obtained from calculations from laboratory experimentation. Results obtained revealed that both the predicted values and calculated values have a linear correlation with an R2 of 96.4%. On this basis the Derived Prediction Model can be said to be valid within the limits of the study.

1. International Journal of Research in Engineering and Science (IJRES)
ISSN (Online): 2320-9364, ISSN (Print): 2320-9356
www.ijres.org Volume 5 Issue 8 ǁ August. 2017 ǁ PP. 40-44
www.ijres.org 40 | Page
Developing A Prediction Model for Tensile Elastic Modulus of
Steel Fiber – Cement Stabilized Laterite Used As Pavement
Material
*
Ekwulo E. O1
. and Igwe E. A2
.
Department of Civil Engineering, Rivers State University, Nkpolu Oroworukwo, Port Harcourt Nigeria
Corresponding author**Ekwulo E. O 1
ABSTRACT: This paper attempts to develop a prediction model that can be used in line with prescribed
laboratory experiments for indirect tensile test such that tensile elastic modulus can be predicted for cement
stabilized lateritic soil reinforced with steel fiber using measured properties of the material. The results of the
tensile elastic modulus obtained from the Derived Prediction Model almost nearly replicates that obtained from
calculations from laboratory experimentation. Results obtained revealed that both the predicted values and
calculated values have a linear correlation with an R2
of 96.4%. On this basis the Derived Prediction Model can
be said to be valid within the limits of the study.
Key words: Steel fiber reinforcement (SFR), tensile elastic modulus, cement stabilized lateritic soil
I. INTRODUCTION
There are two main types of approach in the characterization of materials used in structural design of
flexible pavement: the conventional or empirical method and the rationale or mechanistic design approach.
While the former is still widely used in most developing nations of the world; the latter has gained more grounds
in the developed nations because of its greater reliability in terms of the inherent properties that are of interest to
the highway engineer. The advantage of the latter over the former is that it requires the determination of elastic
and resilient properties of the materials to be used for design which controls the overall behaviour and therefore
performance of the pavement during its useful life [1]. The mechanistic design of roads with cement stabilized
and steel fiber-reinforced lateritic soil requires an adequate knowledge of the elastic properties of the material.
The rationale or mechanistic design methods involve an analytical approach that depends on the laws of
mechanics to predict critical stresses and strains by using the elastic parameters [2]. Furthermore, in mechanistic
design methods of flexible pavement, the materials in each layer of the pavement are characterized by their
modulus of elasticity, E and poisson’s ratio, µ [3]. During characterization the developed tensile and
compressive strains due to repetition of wheel load application are then used for fatigue analysis and permanent
deformation (rutting) assessment [4].
The introduction of steel fibers as reinforcement to lateritic soils used as pavement material is a
relatively new technology for producing a relatively inexpensive material of high strength [5]. Hancork and
Cuthberton [6] studied the effect of fiber and interfacial bond in glass fiber-epoxy resin composites and
concluded that the addition of steel fibers to pavement materials retard the propagation of cracks and sometimes
dislocation of the matrix. In similar studies Shahid and Thom [7] investigated the effect of steel fibers on cement
bound bases. Their result showed that the addition of steel fibers to cement bound material base produced
significant improvement in the tensile properties of the material which further provides extra safety against
longitudinal cracking. The modulus of elasticity whether in tension, compression or shear is another property of
concern in mechanistic design of pavement. Nakagawa et al [8] and Naaman [9] conducted tests for tensile
modulus of elasticity for fiber reinforced cement based composites. Their separate results showed that modulus
of elasticity increased with increase in the fiber content. Poisson’s ratio is another important parameter used in
elastic analysis and design of pavement systems. Studies have revealed that Poisson’s ratio can vary between 0-
5 [10]. Furthermore, stiffer materials tend to have lower Poisson’s ratio than softer materials since the strain
normal to applied stress will be small due to rigidity; thus the ratio of strain normal to the applied stress to that
parallel to the applied stress will be small which describes Poisson’s ratio. In simple terms Poisson’s ratio is
defined as
yx  / (1)
Where, Ɛx = strain normal to the applied stress
Ɛy = strain parallel to the applied stress
µ = Poisson’s ratio
The determination of elastic modulus whether in tension, compression or shear usually involves the
application of equations based on the simple law of motion from physics in the elastic region. However, the

2. Developing A Prediction Model for Tensile Elastic Modulus of Steel……
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parameters of the equation are obtained from laboratory experiments. The indirect tensile test methods have
been used by various researchers in the determination of elastic properties in the analysis and design of
pavement systems in Nigeria – [11]; [3]; [12] and [13].
Adedimila and Emina [14] had done a previous study using the indirect tensile test methods to conduct
the stripping potential of Nigeria’s Asphalt mixtures. Their study revealed that it can be a complement for
Marshall Stability test. Also of interest to the highway engineer is the need to improve the performance of the
individual materials that make-up a road pavement. A typical flexible pavement will consist of a wearing course
comprising of asphalt concrete, base course, sub-base course for weaker soils and the sub-grade. It is pertinent
to say that in most cases these different layers beneath the wearing course do not have adequate material
property quality and therefore will require remediation in many cases. One of such measures of remediation is
stabilization of the base and sub-base courses used as road pavement materials. It is common knowledge that
lateritic soils are the most widely used road pavement materials in road construction as bases and sub-bases
because of its availability. However, in most cases these materials do not meet specification requirements and
therefore need to be improved either by stabilization or other procedures. According to Oguara [2] stabilization
is the modification of soils or aggregates by incorporating materials that will increase load bearing capacity,
firmness and resistance to weathering or displacement under traffic loads. These materials used for the
stabilization are mostly referred to as additives, admixtures, stabilizing agents or stabilizers. Examples include
cement, bitumen and lime. Others include salts such as calcium chloride, sodium chloride, magnesium chloride
and organic compounds. However, for the purpose of the present study steel fibers were used to reinforce
cement stabilized lateritic pavement material.
Ekwulo and Igwe [5] studied the effects of steel fiber reinforcement on cement stabilized lateritic soil
used as pavement material with respect to cracking. Their results revealed that the addition of steel fiber as
reinforcements to the cement stabilized lateritic soil increased tensile strength by 50% and also increased elastic
tensile modulus by 21%. Furthermore, the failure mode for the steel fiber reinforced (SFR) specimen was
gradual as compared to abrupt and brittle failure pattern of the non-SFR specimen. They concluded that steel
fibers were capable of retarding the propagation of cracks in cement stabilized lateritic soil. Although, the
elastic properties of pavement materials can be determined through laboratory testing programs, the purpose of
the present study was to develop a model that can use the properties of the pavement material determined from
the laboratory to predict elastic tensile modulus.
II. METHODOLOGY
2.1 Material properties
The indirect tensile test was used for the determination of the following properties of the steel fiber reinforced
soil-cement:
 Tensile strength
 Modulus of Elasticity (Et) in tension
 Modulus of Elasticity (Ec)
 Horizontal Tensile Strain (Ɛt)
 Vertical Compressive Strain (Ɛc)
2.2 Soil sampling and classification
The soil sample was collected from borrow pit along Umuechem Road in Etche Local Government
Area of Rivers State, Nigeria. The soil classification and physical property tests were carried out in accordance
with relevant British Standard Institute procedure[15] and AASHTO standards [16]. The soil classification test
revealed the following properties:
 Natural Moisture Content = 11.31%
 Liquid Limit = 32%
 Plasticity Index = 15.51%
 Proctor Maximum Dry Density = 1960kg/m3
 AASHTO Classification = A-2-6 soil
2.3 Preparation of Soil Specimen
For the purpose of achieving the objective of the study, specimen preparation was done in accordance
with [17] BY USING 7% cement content [18] and water corresponding to the optimum moisture content.
Furthermore, DUBIC steel fibers (animal wires) of 0.5mm diameter and 40mm long with aspect ratio of 80 were
added to the moist soil - cement paste to produce steel fiber reinforced (SFR) cement stabilized lateritic
pavement material. The composite was then thoroughly mixed in a mixing tray and compacted in a proctor
mould using 2.5kg hammer to produce cylindrical specimens 100mm x 120mm dimension. Steel fiber was
added in varying amounts of 0, 1.2, 1.4, 1.6, 1.8 and 2% respectively. For each fiber content three specimens

3. Developing A Prediction Model for Tensile Elastic Modulus of Steel……
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were prepared in order to have a weighted average. The indirect tensile strength was then carried out in
accordance with Kennedy [19] and Adedimila [20]. Specimens were then cured at 28 days in moist saw-dust in
air-tight plastic containers. The CBR machine was used to apply load through special testing bearings strips
12.7mm wide and 110mm long which was fabricated from a 100mm diameter pipe to enable the seating of the
penetration piston on the test specimen [21]. Tensile properties of the specimens were determined. Also
horizontal tensile strains and vertical compressive strains were measured directly using the DEMEC strain
gauge No. 3463 with sensitivity of 1.97 x 10-5
.
III. RESULTS
The results from the indirect tensile testing of specimens are as presented in Table 1 below;
Table 1: SFR Cement Stabilized Lateritic Soil properties from Indirect Tensile Test
Parameters Fiber Content (%)
0 1.2 1.4 1.6 1.8 2.0
1 Tensile Strength, ST (N/mm2
) = 2p/ᴫtd 0.62 0.65 0.68 0.7 0.55 0.4
2 Poisson’s ratio, µ 0.21 0.24 0.26 0.3 0.27 0.25
3 Modulus of Elasticity in Tension, ET (N/mm2
) 36,400 38,400 42,000 46,100 30,300 21,500
4 Modulus of Elasticity in Compression, Ec
(N/mm2
) 4,580 5,720 6,890 8,540 4,350 4,170
5 Horizontal Tensile Strain, Ɛt (x 10-5
) 2.31 2.62 2.7 3.16 2.73 2.31
6 Vertical Compressive Strain, Ɛc (x 10-5
)
16.89 17.16 18.56 19.41 16.08 14.04
IV. MODEL DEVELOPMENT
The following steps were undertaken during the process of developing a prediction model for Tensile
Elastic Modulus for the SFR Cement Stabilized Lateritic Soil:
1. Model proposal: the following model was proposed for the prediction of tensile elastic modulus for SFR
Cement Stabilized Lateritic Soil:   caE
bS
T t
T
 
*
( 2)
Where: ET = Tensile Elastic Modulus
ST = Tensile strength of specimen
µ = Poisson’s ratio
Ɛt = Horizontal tensile strain
a, b and c are coefficients to be statistically determined
2. Measure tensile strain for each specimen at failure
3. Measure Poisson’s ratio for each specimen at failure
4. Determine tensile strength of each specimen at failure
5. Calculate tensile elastic modulus for each specimen at failure
6. Write a non-linear regression equation that satisfies the condition of the general form of the proposed model
7. Input stringed variables into the SPSS software for non linear analysis
4.1 Developing Proposed Model Using Non Linear Regression Approach in SPSS
A non linear model is one in which at least one of the parameters appear nonlinearly. More formally, in
a nonlinear model, at least one derivative with respect to a parameter should involve that parameter. To solve
the non linear regression using SPSS, the variables (dependent and independent) were first of all collated into
different cells in the “Data View” dialogue box. Next, these variables were stringed and coded into another
dialogue box called the “Variable View Cell”. Finally model syntax was developed that satisfies the condition of
the general form of the model proposed.
4.2 Non Linear Model Syntax
The non linear model syntax is of the form as shown below;
 
   caE b
bS
T t
T
 **
***
* 

(3)
Equation 3 is the non linear syntax model that corroborates the general form of the proposed model in
Equation 2 used for analysis in the SPSS program. Furthermore, in SPSS the command (**) means raising a
variable to the power of the coefficient in the same bracket while the command (*) means multiplication. By
applying Equation 3 in the SPSS program using results from Table 1 the experimental coefficients were
determined as follows, a = 1.30; b = 1.216; c = 12,620 [See Appendix A: Table 1 a - c].
By applying the coefficients obtained the resulting prediction model equation in syntax form becomes;

4. Developing A Prediction Model for Tensile Elastic Modulus of Steel……
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 
   620,12*3.1 216.1**
216.1***
 t
TS
TE 

(4)
The actual prediction model can thus be written as;
  620,123.1
216.1*
 t
TS
TE 

(5)
4.3 Validation of Model
In order to validate the fairness of the derived model, values from indirect tensile test results in Table 1
above were inputted into Equation 5 to determine predicted values of tensile elastic modulus. The values
obtained from the predicted model for tensile elastic modulus were then compared with that calculated from
laboratory experimentation as in Table 2 and Figure 1. The results of their correlation revealed that the
predictive model developed closely simulated calculated values of tensile elastic modulus having an R2
value of
0.964.
Table 2: Comparison of Calculated and Predicted Tensile Elastic Modulus, ET
S/N Fibre Content (%) Calculated Tensile Elastic Modulus Predicted Elastic Modulus
1 0 36,400 34,712.36
2 1.2 38,400 37,977.43
3 1.4 42,000 44,179.36
4 1.6
46,100 45,208.58
5 1.8 30,300 32,710.34
6 2.0 21,500 21,719.28
Figure 1: Calibration of Predicted and Calculated Tensile Elastic Modulus
V. DISCUSSION
From figure 1, it was observed that the results from the prediction model closely replicated that
calculated from laboratory experimentation. Also the similarity of their correlation is such that they are linearly
related with the expression as in Equation 6 below with an R2
value of 96.4%.
    1611963.0  calculatedTpredictedT EE
6
VI. CONCLUSION
From the foregoing based on the laboratory experiments carried out, results obtained and analysis as presented
in the sections above the following conclusions can be made;
1. Since the Derived Prediction Model for Tensile Elastic Modulus from Equation (5) closely simulates
results calculated from laboratory experimentation; it can thus be accepted as a means for predicting
Tensile Elastic Modulus under similar conditions.
2. The general form of the Derived Prediction Model can be written in simple terms as in Equation 2 above.
3. The relationship between the derived prediction model for tensile elastic modulus and the calculated
tensile elastic modulus from laboratory experimentation is generally linear and expressed as in Equation 6.

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*Ekwulo E. O1. "Developing A Prediction Model for Tensile Elastic Modulus of Steel Fiber – Cement
Stabilized Laterite Used As Pavement Material." International Journal of Research in Engineering and
Science (IJRES) 5.8 (2017): 40-44.